No, I know of no Earth Scientist who would
contest the idea that continents are moving (along
with the larger plates that they are part of).
That doesn't mean that some uninformed people
think continental drift is a hoax, but then again,
some people mistakenly believe that Earth is flat.
Sometimes even the strongest scientific ideas
fail to convince everyone.

Answer 2:

No, continental drift is such a thoroughly
supported theory that nobody seriously doubts
it. There are still some unanswered questions
about exactly what causes it and how it happens,
though.